In this work, we shall review two recent constructions, [1]}, [2]}, that address the above two questions in turn. Our starting point will be to regard the space \(M\)  as a coset of the conformal group by a certain parabolic subgroup \(P\) . Any function on \(M\)  thus can be lifted to a function on the group that is (left) covariant with respect to \(P\) . As we will see, the lifted function is then nothing but a vector in a principal series representation of \(G\) .
